Question

The difference between the compound interest, compounded annually and the simple interest in a certain sim for 2 years at 4% per annum is ₹20. Find the sum.​

Answer 1

Answer:

The amount is 12500 rupees.

Step-by-step explanation:

Let $I_s$ be the simple interest on a particular amount $P$ at a rate $R\%$ for $N$ years.

Then

$I_s=\dfrac{PNR}{100}$

The compound interest $I_c$

$I_c=P(1+\frac{R}{100})^N-P$

Given that, the difference of these interests is 20 rupees when the rate of interest is 4% per annum for two years.

Thus we obtain,

$\implies I_c-I_s=20\\\\\implies P(1+\frac{R}{100})^N-P-\dfrac{PNR}{100}=20\\\\\implies P(1+\frac{4}{100})^2-P-\dfrac{P\times 2\times 4}{100}=20\\\\\implies 1.04^2P-P-0.08P=20\\\\\implies P(1.04^2-1-0.08)=20\\\\\implies 0.0016P=20\\\\\implies P=\dfrac{20}{0.0016}=12500$

So the amount for which the difference of compound interest and simple interest is 20 is 12500 rupees.

Answer 2

Answer:

12,500

Step-by-step explanation:

Given the difference between compound interest and simple interest is 20

Principle = 'p'

Time = 2 yrs

Rate of interest = 4%

Difference  = 20

$P[(1+i)^n-1] - p * i * t = 20$

$P[(1+0.04)^2-1] - p*0.04 * 2 = 20$

$P[(1.04)^2-1] - 0.08p = 20$

$0.0816p - 0.08p = 20$

$0.0016p = 20$

$P = \frac{20}{0.0016}$

P = 12,500

Hence the sum is 12,500